Trigger JavaScript on a page (e.g. Toast notification) via API Callback - can it be done with Livewire?

I'm not understanding the interaction between Livewire, Laravel PHP, JavaScript events, and broadcasting.

For my application I want to trigger JavaScript on a page, say for example show a Toast notification, when I receive a post request from a 3rd party website. I believe I can do this with laravel-sockets and Laravel Echo but the overhead seems huge just to get notifications working.

I guess the part I don't exactly understand is how would a PHP backend (from an arbitrary page or route) communicate directly to an HTML page and trigger JavaScript on that page...

Longer explanation:

1. My supplier give me JavaScript to launch an iFrame that connects to the Bank.

To launch the iFrame the supplier's JavaScript header is this:

bankLinkBtn.addEventListener('click', function() {
                window.banklink.open({
                        fastLinkURL: '<?php echo $bankLinkURL; ?>',
                        jwtToken: 'Bearer <?php echo $token; ?> ',
                        params: {
                            workflowFlow: 'Consolidation',
                            callback: '<?php echo $callback; ?>',
                        },
                        onSuccess: function(data) {                            
                            console.log(data);
                        },
                        onError: function(data) {                            
                            console.log(data);
                        },
...

1. The route in my web application is this:

Route::get('/bank/callback', [Controllers\BankApiController::class, 'callback'])->name('bank.callback');

What I want to do in the callback method on the Bank API Controller is to refer back to the original JavaScript page and trigger a toast notification, say "Linking complete!".

So the direct path that seems unclear in my mind is:

Can one set an API route direct to a Livewire component page?

Can I "anywhere" on my Laravel app "contact" this Livewire page and do something with the JavaScript?

Or do I have to use Websockets and event broadcasting?